Coherent Backscattering from Multiple Scattering Systems - KOPS ...

5.1 Conservation of energy in coherent backscattering
1
kl* = 2
kl* = 4
kl* = 10
0.8
cooperon
0.6
0.4
0.2
0
−90 −60 −30 0 30 60 90
scattering angle [deg]
Figure 5.5: Old and new theory. The graph shows the cooperon calculated with
eqn. 2.15 (dashed lines) and including the additional contribution given in eqn. 5.7
(solid lines). The dotted lines give the enhancement of the cooperon for the new theory
(for the old theory the enhancement is always equal to 1). Parameters: wavelength
λ = 590 nm, diffusion coefficient D = 15 m2 /s, reflectivity R = 0.5.
The fit parameter a is therefore obtained by numerical integration of
a =
0
∫ π/2
0
∫ π/2
I (A)
c
1
(kl ∗ ) 2 ·
· sin θ dθ
µ · sin θ dθ
µ + 1
After normalization analogous to eqns. 2.13, the additional contribution to the cooperon finally
becomes
α (B+C)
c
8π · a
= −
3 k 2 l ∗ (l ∗ + 2z 0 ) ·
µ
µ + 1
(5.7)
does not contribute at a specific angular value but it is rather spread out over the
whole angular range, similar to the diffuson. In particular it reduces the enhancement of the
coherent backscattering cone, so that the total cooperon α (A)
c
α (B+C)
c
+ α (B+C)
c at the conetip at θ = 0
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